Question: Simplify the following expression: $ y = \dfrac{-4}{9} + \dfrac{5k + 1}{k - 9} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 9}{k - 9}$ $ \dfrac{-4}{9} \times \dfrac{k - 9}{k - 9} = \dfrac{-4k + 36}{9k - 81} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{5k + 1}{k - 9} \times \dfrac{9}{9} = \dfrac{45k + 9}{9k - 81} $ Therefore $ y = \dfrac{-4k + 36}{9k - 81} + \dfrac{45k + 9}{9k - 81} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{-4k + 36 + 45k + 9}{9k - 81} $ $y = \dfrac{41k + 45}{9k - 81}$